Skip to main content

8. Maximum Depth of Binary Tree

easyAsked at Mercury

Compute the maximum depth (longest root-to-leaf path) of a binary tree.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given the root of a binary tree, return its maximum depth. Maximum depth is the number of nodes along the longest path from the root down to the farthest leaf.

Constraints

  • Node count in [0, 10^4]
  • -100 <= Node.val <= 100

Examples

Example 1

Input
root = [3,9,20,null,null,15,7]
Output
3

Example 2

Input
root = [1,null,2]
Output
2

Approaches

1. BFS level count

Walk levels with a queue and count rounds until empty.

Time
O(n)
Space
O(n)
let q=root?[root]:[]; let d=0;
while(q.length){const n=[]; for(const x of q){ if(x.left)n.push(x.left); if(x.right)n.push(x.right);} q=n; d++;}
return d;

Tradeoff:

2. Recursive max(left, right) + 1

Depth = 1 + max(depth(left), depth(right)); empty subtrees return 0. One-line clean recursion.

Time
O(n)
Space
O(h)
function maxDepth(root) {
  if (!root) return 0;
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
}

Tradeoff:

Mercury-specific tips

Mercury asks depth questions to gauge how you reason about hierarchical KYC pipelines — each subsidiary entity adds a tier and depth gates which compliance reviewer level approves.

Solve it now

Free. No sign-up. Python and JavaScript run instantly in your browser.

Output

Press Run or Cmd+Enter to execute

Practice these live with InterviewChamp.AI

Drill Maximum Depth of Binary Tree and other Mercury interview questions under real-loop conditions with instant feedback on your reasoning, complexity claims, and code.

Practice these live with InterviewChamp.AI →